Exam 10: Derivatives: Risk Management With Speculation, Hedging, and Risk Transfer  

You hold a portfolio made of French stocks and worth €10 million. The beta ( $\beta$ ) of this portfolio relative to the CAC index is 1.5. The interest rate for the euro is 4% for all maturities and the annual dividend yield is 2%. The spot value of the CAC index on January 1, 2000, is 5,000. A CAC contract has a size of €10 for each index point. a. What should be the future price of the CAC contract with a three-month maturity? b. You fear a fall in the French stock market. What should be your hedge ratio? How many contracts do you buy/sell?

LTCM observed the following ten-year swap spreads on July 1, 1998. You remember that U.S. dollar interest swaps (fixed rate against LIBOR three-month) are quoted as a spread over the Treasury yield (so the fixed rate on the swap is equal to the interest rate on Treasury bonds for the same maturity plus the quote spread). LTCM believes that the normal spread is 40 bp (basis points). The current spread of 80 bp is expected to converge back to normal in three months. If you borrow securities, you have to deposit as collateral an equivalent amount of cash that is marked-to-market. For example, if you borrow a security that is worth 100, you have to deposit 100; if the value of the security increases to 110, you have to deposit 10 more. Swaps are also marked-to-market and free of default risk. a. What arbitrage using Treasury bonds and swaps could you put in place if you believe that the spread will revert back to its normal level? Be very precise and assume you do the above arbitrage for $100 million. How much of LTCM capital is invested in the arbitrage? b. Suppose that the spread is still at 80 bp on October 1, but that Treasury yields have moved up by 40 bp on October 1 (reset date for the floating leg). What is your gain/loss in dollars? [You only need to provide a rough estimate assuming that the sensitivity (duration) on the Treasury bond and fixed leg of the swap is equal to 10.] c. Other scenario: How much would you gain (from July 1) if Treasury yields do not move, but the spread reverts back to 40 bp three months later on October 1 (reset date for the floating leg)? [You only need to provide a rough estimate assuming that the sensitivity (duration) on the Treasury bond and fixed leg of the swap is equal to 10.]

An Italian corporation enters into a two-year interest rate swap in euros on April 1, 2000. The swap is based on a principal of €100 million, and the corporation will receive 7% fixed and pay six-month Euribor. Swap payments are semiannual. The 7% fixed rate is quoted as an annual rate using the European method, so the implied semiannual coupon is 3.44% [since (1.0344)² = 1.07]. Two years later, the swap is finally settled, and the following Euribor rates have been observed: Apr. 1, 2000 Oct. 1, 2000 Apr. 1, 2001 Oct. 1, 2001 Apr. 1, 2002 6.5\% 7.5\% 8\% 7.5\% 6\% a. What have the swap payments or receipts for the corporation been on each swap payment date? b. The same Italian corporation also entered another two-year interest rate swap in euros on April 1, 2000. The swap is based on a principal of €100 million, and the corporation contracted to receive 7% fixed and pay six-month Euribor. On this swap, the payments are annual. Hence, the two successive six-month Euribor are compounded. Assuming that the Euribor rates given in the previous problem have been observed, what have the two annual swap payments been?

You will receive $10 million at the end of June and will invest it for three months on the Eurodollar market. The current three-month Eurodollar rate is 6%, and you are worried that the rate will drop by the end of June. Here are some market quotes: $\bullet$ Eurodollar LIBOR futures, June delivery: Price 94%. $\bullet$ Call eurodollar, June expiration, strike price 94%: Premium 0.4%. $\bullet$ Put Eurodollar, June expiration, strike price 94%: Premium 0.4%. The contract sizes are $1 million. a. Should you buy or sell futures to hedge your interest rate risk? b. Should you buy (or sell) calls (or puts) to insure a minimum rate at the time you will invest your money? What is this rate? c. In June, the Eurodollar rate has moved to 4%. What is the result of your strategies using futures and using options? d. What if the rate is equal to 8% in June?

To capitalize on your expectation of a 10% gold price appreciation, you consider buying futures or option contracts to speculate. The spot price of gold is $400. Near-delivery futures contracts are quoted at $410 per ounce with a margin of $1,000 per contract of 100 ounces. Call options on gold are quoted with the same delivery date. A call with an exercise price of $400 costs $20 per ounce. The rate of return on your speculation will be the return on your invested capital, which is the initial margin for futures and the option premium for options. a. Based on your expectation of a 10% rise in gold price, what is your expected return at maturity on futures contracts? b. Based on your expectation of a 10% rise in gold price, what is your expected return at maturity on option contracts? c. Simulate the return of the two investments for various movements in the price of gold.

A German investor holds a portfolio of British stocks. The market value of the portfolio is £20 million, with a $\beta$ of 1.5 relative to the FTSE index. In November, the spot value of the FTSE index is 4,000. The dividend yield, euro interest rates, and pound interest rates are all equal to 4% (flat yield curves). a. The German investor fears a drop in the British stock market (but not in the British pound). The size of FTSE stock index contracts is 10 pounds times the FTSE index. There are futures contracts quoted with December delivery. Calculate the futures price of the index. b. How many contracts should you buy or sell to hedge the British stock market risk? c. You believe that the capital asset pricing model (CAPM) applies to British stocks. The expected stock market return is 10%. What is the expected return on this portfolio before and after hedging? d. You now fear a depreciation of the British pound relative to the euro. Will the strategies above protect you against this depreciation? (Assume that the margin on the futures contract is deposited in euros.) e. The forward exchange rate is equal to 1.4 € per £. How many pounds should you sell forward?

The French futures market, MATIF, trades Euribor contracts. The Euribor is the three-month interbank interest rate on euros. The contract size is €1 million, and the margin is €3,000. On January 10, March futures trade at 90.74%. Options on the Euribor futures contract are also listed. The premiums (in %) on March options are as follows: Strike Price Call Put 90.40 0.30 0.06 90.80 0.17 0.18 91.00 0.09 0.34 A few days later (January 14), the futures price moves to 89.50. a. What is the gain or loss, in euros, for someone who sold a futures contract on January 10? b. What is the return, as a percentage of the initial investment (margin)? c. Are all option premiums quoted on January 10 reasonable? d. You know that you will have to borrow €10 million in March and fear a rise in interest rates. What are the maximum borrowing rates that you can insure using the various options? e. To cap your borrowing rate, you decide to use options with a strike price of 90.80. How many calls (or puts) should you buy (or sell)? On January 14, the premium on the call March 90.80 moves to 0.02, and the premium on the put March 90.80 moves to 1.33. f. What is the € profit (or loss) on your option position? g. What is the rate of return on your option position?

You would like to protect your portfolio of British equity against a downward movement of the British stock market. a. What are the relative advantages of stock index futures and options? b. Should you prefer in-the-money or out-of-the-money options?

Four years ago, a Swiss firm contracted a currency swap of US$100 million for 250 million Swiss francs (SFr), with a maturity of seven years. The swap fixed rates are 8% in dollars and 4% in francs, and swap payments are annual. The Swiss firm contracted to pay dollars and receive francs. The market conditions are now (exactly four years later) as follows: Spot exchange rate: 2.00 Swiss francs/U.S. dollar. Term structure of zero swap rates: Maturity Years U.S. Dollar \% (ann.) Swiss Franc \% (ann.) 1 9 5 2 9.5 5.75 3 10 6 4 10.25 6.25 5 10.75 6.5 6 11 7 7 11.5 7.5 a. What should the swap payment (receipt) be at the end of the fourth year, that is, today? b. Right after this payment, what is the swap market value for the Swiss firm?